Magnetotelluric transfer function distortion assessment using Nyquist diagrams

Abstract

Magnetotelluric (MT) inversion is using impedance data as input data, which is traditionally presented via the apparent resistivity and impedance phase. Since high-quality MT data are necessary to improve the reliability of inversion results, the distortions in the curves should be assessed and removed. Usually, this smoothing procedure acts individually on the apparent resistivity and phase and does not consider the dispersion relationship between the real and imaginary parts of the impedance. Therefore, how to assess the distortion while retaining the inherent relationship in the impedance should be addressed. In this study, Nyquist diagrams were used as a tool to illustrate the inherent feature of the MT complex response. The MT impedances of 2-D and 3-D models were computed and illustrated in the corresponding diagrams. From these curves, we found that the Nyquist curves or part of them are continuous and smooth. When the model is 1-D or 2-D, Zxy and Zyx try to stretch around a line at a 45° slope, whereas in the 3-D case, the Nyquist diagrams of the full impedance elements rotate clockwise from low to high frequencies. If the frequency is high or low enough, the curves of Zxx and Zyy become approximate ellipses. The phases of Zxx and Zyy are also out of scope (−π,π), which is beyond the traditional knowledge of the phase, which making data distortion removal in the phase confusing. Cole-Cole model could be used to explain above features. And these features behind the Nyquist diagrams could be used as tools to guide the distortion removal in the MT complex response in the field. When MT impedance data are not severely distorted, it is possible to recover high-quality data when obeying the following two rules: (1) both the amplitude and phase should be smooth and (2) the Nyquist curve of the complex response should also be smooth or at least smooth in segments.